Question

Where t is in seconds and the coefficients have the proper units for r to be in metres (a) Find v(t) and a(t) of the particle. (b) Find the magnitude and direction of v(t) at t = 1.0 s.

Answer 1

Dear Student,
As given in the question, $$\begin{gathered} v\left(t\right)=\frac{dr}{dt}=\frac{d}{dt}(3.0t\hat{i}+2.0t^2\hat{j}+5.0\hat{k}) \\ =3.0\frac{d}{dt}\left(t\right)\hat{i}+2.0\frac{d}{dt}\left(t^2\right)\hat{j}+5.0\frac{d}{dt}\left(1\right)\hat{k} \\ =3.0\hat{i}+4.0\hat{j}+0\hat{k}[becausethedifferentiation \\ ofcons\tan t=0] \end{gathered}$$

Regards